渐近边界条件在轴对称无界高压静电场计算中的应用

The Application of the Asymptotic Boundary Conditions Technique in the Numerical Analysis of Axisymmetrical Unbounded High-Voltage Static Field

将渐近边界条件技术引入到有限元数值计算方法中，计算了具有轴对称特性的两种典型高压电极无界静电场问题。结果表明：采用渐近边界条件后，计算结果具有较高的精度，可以尽可能地缩小人工边界的设置范围；该技术保留了有限元法的显著优点—系数矩阵的高度稀疏性和对称性；对于长宽比值较大的窄形电极问题，如采用人工边界为矩形的渐近边界条件，将会使计算效率显著提高。

This paper presents a finite element formulation for the solution of axisymmetrical unbounded static fields of two typical high-voltage electrodes using asymptotic boundary conditions (ABC). The numerical results show that (1)ABC technique yields more accurate results and can reduce the region of artificial boundary as much as possible. (2) ABC technique preserves the sparsity and symmetry of the finite element matrix. (3) For the electrode with large aspect ratios, the calculation efficiency will be improved rapidly if the rectangular artificial boundary is adopted.